Honest priest found in cocktail bar by Luddite extremists (8)
I believe the answer is:
reliable
'honest' is the definition.
(I know that honest can be written as reliable)
'priest found in cocktail bar by luddite extremists' is the wordplay.
'priest' becomes 'eli' (biblical figure).
'found in' is an insertion indicator.
'cocktail' indicates an anagram.
'by' is a charade indicator (letters next to each other).
'extremists' suggests removing the centre (letters on the extreme ends of the word).
'luddite' with its centre taken out is 'le'.
'bar' anagrammed gives 'rab'.
'eli' inserted inside 'rab' is 'reliab'.
'reliab'+'le'='RELIABLE'
(Other definitions for reliable that I've seen before include "Dependable, can be trusted" , "Dependable, trustworthy" , "Faithful" , "Unfailing" , "Trusty" .)